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This letter reports a compact behavioral model for the hysteretic conduction characteristics of Al/Gd 0.1 Ca 0.9 MnO 3 (GCMO)/Au resistive switching devices suitable for SPICE simulations. The devices are nonvolatile, forming-less, compliance-free, and self-rectifying multistate memristive structures which makes them of maximum interest for neuromorphic computing and memory applications. The proposed model relies on two coupled equations, one for the electron transport and a second one for the vacancy displacement. First, the fixed and variable current components that contribute to the total electronic flow are identified and modelled. They are tunneling and diode-like conduction with series resistance through the thin sub-oxide layer formed at the GCMO/Al interface in combination with filamentary conduction. Second, the memory equation accounts for the reversible movement of vacancies that causes the generation and self-healing of these micro-filaments. Importantly, the proposed model considers a novel approach for solving the internal state of the device based on the so-called generalized quasi-static hysteron whose application can be extended to other structures and dynamics in addition to the ones discussed here.